Having cared for my parents and my husband's parents into their old age, I can attest to the fact that there were times when we had to visit hospitals or doctor's offices and the physicians wanted to refer them to social workers so that they could be placed under government supervision. I was appalled how easy it was for social services to step in when there was no need.
The real costs are in nursing home care. Sometimes it's necessary, but most times the elder doesn't want to go there. There have to be other ways that are more economical.
Your theory is great, but “seniors” have been led to believe by our government that Medicare would be there for them. Most don’t have the resources to purchase the type of insurance you mention. Now consider that your typical 50 year old has paid into this fraud for 30 yrs already so he/she’s unlikely to start diverting significant funds to private insurance.
So the logical result is rationing and death panels.